Abstract The origin of the heliospheric magnetic flux on the Sun, and hence the origin of the solar wind, is a topic of hot debate. While the prevailing view is that the solar wind originates from outside the coronal streamer helmets, there also exists the suggestion that the open magnetic field spans a far wider region. Without the definitive measurement of the coronal magnetic field, it is difficult to unambiguously resolve the conflict between the two scenarios. We present two 2-dimensional, Alfvénic-turbulence-based models of the solar corona and solar wind, one with and the other without a closed magnetic field region in the inner corona. The purpose of the latter model is to test whether it is possible to realize a picture suggested by polarimetric measurements of the corona using the Fe XIII 10747 Å line, where open magnetic field lines seem to penetrate the streamer base. The boundary conditions at the coronal base are able to account for important observational constraints, especially those on the magnetic flux distribution. Interestingly, the two models provide similar polarized brightness (pB) distributions in the field of view (FOV) of SOHO/LASCO C2 and C3 coronagraphs. In particular, a dome-shaped feature is present in the C2 FOV even for the model without a closed magnetic field. Moreover, both models fit the Ulysses data scaled to 1 AU equally well. We suggest that: 1) The pB observations cannot be safely taken as a proxy for the magnetic field topology, as is often implicitly assumed. 2) The Ulysses measurements, especially the one showing a nearly uniform distribution with heliocentric latitude of the radial magnetic field, do not rule out the ubiquity of open magnetic fields on the Sun.

Keywords Sun: corona — Sun: magnetic fields — solar wind

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